关键词: 空间碎片群, 轨道预报, 多项式代理, 切比雪夫多项式, 半解析方法

Abstract: Rapid and precise orbit determination and prediction for large-scale debris cluster serve as crucial foundations for enhancing collision warning capabilities. However, existing high-precision numerical methods rely on small-step, object-wise integration, leading to poor scalability with respect to the number of debris objects and limiting efficiency for large-scale debris propagation. To address this issue, this paper proposes an efficient semi-analytical orbit prediction method for space debris cluster based on polynomial surrogate. Firstly, this method constructs a high-order polynomial surrogate model mapping initial orbital states of debris to orbital states at any given time using Jet Transport and Chebyshev approximation. Then, the feedback-accelerated Picard iteration method with large-step parallel computation is introduced to further improve efficiency. Moreover, a nominal orbit selection strategy based on phase-space partitioning is developed to suppress error divergence in the polynomial surrogate model near debris cluster boundaries. Finally, using initial debris values generated from the NASA standard breakup model, short-term orbit prediction simulations for different space debris clusters in LEO, HEO, and GEO scenarios are conducted. Results show that, when average prediction error is set within 1 meter, the proposed JT-Chebyshev method improves computational efficiency by over 150 times compared to the Monte Carlo method.

Key words: space debris cluster, orbit prediction, polynomial surrogate, Chebyshev polynomial, semi-analytical method